The sum of first 10 terms of an AP is 4 times the sum of its first 5 terms. Then what is the ratio of the first term and the common difference?
Answers
Answered by
8
Given: S10 = 4 S5
We know Sn = n/2 [2a + (n-1)d], where a= first term of A.P. and d = common difference
10/2 [2a + (10-1)d] = 4 * 5/2 [2a + (5-1)d]
2a + 9d = 2 [2a + 4d]
2a + 9d = 4a + 8d
9d - 8d = 4a - 2a
d = 2a
a/d = 1/2
We know Sn = n/2 [2a + (n-1)d], where a= first term of A.P. and d = common difference
10/2 [2a + (10-1)d] = 4 * 5/2 [2a + (5-1)d]
2a + 9d = 2 [2a + 4d]
2a + 9d = 4a + 8d
9d - 8d = 4a - 2a
d = 2a
a/d = 1/2
Similar questions